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We repeated the analysis of this device using the complex dielectric constant of silver, not merely the real part. When we include even optimistic numbers for the imaginary component of epsilon, our calculations yield an E2 enhancement of approximately 40. As opposed to an enhancement on the order of thousands which was achieved in a lossless medium, the more realistic case is much less impressive. Reference 38 took the effects of electron scattering at the surface into account through the use of the Hydrodynamic Model40, but ignored the more basic first order absorption effects.
This planar structure supports propagating plasmons, however it suffers from diminished grain size when the metal film is made to be thin. 34 Electrons in a nanometer-scale silver film will suffer from much greater grain-boundary scattering losses than those in thick silver. Thus, the insulator-metal-insulator system is inherently lossier70. This problem becomes catastrophic as the film thickness reduces to the scale of monolayers. Electron energy loss spectroscopy experiments71 have shown that ultra-thin silver films form grains that completely localize the plasmons, not allowing them to propagate at all.
This effect is most prominent at large wave-vectors. The simple wave equation, as shown in Equation (2-8), dictates why the skin depth must become very small. At large wave-vectors, the term representing the light line is negligible and K ≈ k . Because the term K is the rate of exponential decay into the medium, the skin depth is then 1/K. under the large-k approximation, this is equal to the plasmon wavelength (λp) divided by 2π and is therefore forced to become very small as the k vector becomes very large.